in a domain of unit length (\(L=1\) ) with periodic boundary conditions, with viscosity \(\nu =8 \cdot 10^{-4}\) . This parameter set results in what is known as Burgers turbulence or Burgulence [1]}.
We solve this equation using a pseudospectral Runge-Kutta Crank-Nicolson scheme as described in [2]}. The state \(u\)  is then represented in \(\mathbb {R}^{512}\)  by \(v\)  sampled at equidistant points in the domain.
We construct 1000 random initial conditions for training the models and 100 random initial conditions for testing model performance. We then evolve each initial condition over the interval \([0,5]\)  sampling every \(0.05\)  time units. This results in \(10^4\)  total snapshots of data used for training. All figures compare test data to model reconstruction of the test data.
